α-stable Lévy processes entering the half space or a slab

2024/07/29 by Andreas E. Kyprianou, Kyprianou, Andreas E., Sonny Medina +3
Economics, Econometrics and Finance · #60G18 #60G51 #60G52 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2407.20394

openalex publication_date 2024/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recent fluctuation identities for α-stable Lévy processes have decomposed paths using generalised spherical polar coordinates revealing an underlying Markov Additive Process (MAP) for which a more advanced form of excursion theory can be exploited. Inspired by this approach, we give a different decomposition of the d-dimensional isotropic α-stable Lévy processes in terms of orthogonal coordinates. Accordingly we are able to develop a number of n-tuple laws for first entrance into a half-space. We also numerically construct the law of first entry of the process into a slab of the form (-1, 1)× ℝ^d-1 using a walk-on-half-spaces Monte Carlo approach.

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